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A292843
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Number of sets of nonempty words with a total of n letters over 9-ary alphabet.
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3
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1, 9, 117, 1542, 19404, 239481, 2900802, 34609797, 407615175, 4747112731, 54743025339, 625791326688, 7097863351275, 79938092898747, 894514969436076, 9951032414168964, 110103625982603466, 1212181195307220126, 13283829023674846878, 144946503880942833774
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{j>=1} (1+x^j)^(9^j).
a(n) ~ 9^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(9^(m-1)-1)) = 0.058648829660552563553047659756831342987... - Vaclav Kotesovec, Sep 28 2017
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MAPLE
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h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1)*binomial(9^i, j), j=0..n/i)))
end:
a:= n-> h(n$2):
seq(a(n), n=0..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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